The FTSE 250 group is currently “evaluating a wide range of separation options” for the division, which transports and stores money on behalf of its customers.
G4S said it was taking steps to “commence the process of separation in the second half” of 2019.
Analysts at Royal Bank of Canada think the cash business, which saw revenues fall 9% to £1.1bn in 2018, could fetch as much as £1.6bn.
There are more options on the table than just a straight sale though, with G4S hinting that it could look to spin off the division and float it on a stock exchange.
The company, which also has the contract to provide security at Area 51, made the announcement alongside its full-year results.
Revenue fell 4% to £7.51bn in the 12 months ended 31 December (2017: £7.83bn), while earnings plunged 65% to £82mln (2017: £237mln).
The drop-off in profitability reflected a £100mln settlement in California and a £35mln charge for pension equalisation regulation in the UK.
G4S shares opened sharply lower on Tuesday morning, although they recovered most of their ground in the afternoon session. At 2.30pm, the stock was down 0.8% to 206.5p.